I am going through the same process right now. I settled on an 18 foot lowboy from ProLine with all the options - total weight of trailer with options (cabinets, battery, winch, e-track, etc.) will be about 2,900 lbs.
https://nhtrailers.com/car-haulers/7000-gvwr-lowboy/
I went with the 18' so that I had options of putting a larger car in the trailer if I ever had to or wanted to. A 16 footer would have been fine for the Cobra -especially with the V-nose.
Went to visit them and was very impressed - family owned, built right here in NH, no dealers or mark so priced very competitively.
With Cobra and gear, I figure total weight will be about 5,600 lbs. I do not have a truck nor do I want one as an everyday driver so I will be towing with my Jeep GC with Hemi and tow package.
That's my story and I'm sticking to it...
I was concerned about trailer sway with the longer trailer and shorter wheelbase SUV. I will be investing in the ProPride Hensley style hitch:
https://www.propridehitch.com/propri...UaAp7REALw_wcB
Not cheap but I will feel a lot better having this hitch with my setup.